Adam starts with the number z=1+2i on the complex plane. First, he dilates z by factor of 2 about the origin. Then, he reflects it across the real axi

Reggie 2020-11-08 Answered
Adam starts with the number z=1+2i on the complex plane. First, he dilates z by factor of 2 about the origin. Then, he reflects it across the real axis. Finally, he rotates it 90 counterclockwise about the origin. The resulting complex number can be written in form a+bi where a and b are real numers. What is the resukring complex number?
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wornoutwomanC
Answered 2020-11-09 Author has 81 answers
Adam starts with complex number Z=1+2i
After getting dilated by a factor of 2 , Z becomes 2+4i
Then the number is reflected across the real axis, so the number becomes 2-4i
Now, the resulting number is rotated 90 anticlockwise .
we know if point (a, b) is rotated anticlockwise by the angle α, then we get point (acosαbsinα,bcosα+asinα) so (2,-4) after gets rotated 90°anticlockwise becomes (2cos90+4sin90,4cos90+2sin90)=(4,2).
So, the resulting complex number is 4+2i
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